Cluster tilting for one-dimensional hypersurface singularities
Cluster tilting for one-dimensional hypersurface singularities
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DOI：
10.1016/j.aim.2007.10.007
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发表时间：
2007-04
影响因子：
1.7
通讯作者：
I. Burban;O. Iyama;B. Keller;I. Reiten
中科院分区：
文献类型：
--
作者：
I. Burban;O. Iyama;B. Keller;I. Reiten
本文利用簇倾斜理论的方法研究了一维超曲面奇点上的Cohen-Macaulay模及其与结合代数表示理论的关系。利用高次几乎分裂序列和双有理几何的结果，给出了倾斜星系团存在的一个判据，并利用同调方法给出了倾斜星系团的完整描述。我们得到了一类满足τ2= id的有限维对称的2-CY倾斜代数，特别地，我们计算了简单和极小椭圆曲线奇点的2-CY倾斜代数.
In this article we study Cohen–Macaulay modules over one-dimensional hypersurface singularities and the relationship with the representation theory of associative algebras using methods of cluster tilting theory. We give a criterion for existence of cluster tilting objects and their complete description by homological methods, using higher almost split sequences and results from birational geometry. We obtain a large class of 2-CY tilted algebras which are finite-dimensional symmetric and satisfy τ2=id. In particular, we compute 2-CY tilted algebras for simple and minimally elliptic curve singularities.